Concentration of the first eigenfunction for a second order elliptic operator

We study the semi-classical limits of the first eigenfunction of a positive second order operator on a compact Riemannian manifold when the diffusion constant $\epsilon$ goes to zero. We assume that the first order term is given by a vector field $b$, whose recurrent components are either hyperbolic points or cycles or two dimensional torii. The limits of the normalized eigenfunctions concentrate on the recurrent sets of maximal dimension where the topological pressure \cite{Kifer90} is attained. On the cycles and torii, the limit measures are absolutely continuous with respect to the invariant probability measure on these sets. We have determined these limit measures, using a blow-up analysis.Comment: Note to appear in C.R.A.

Stellar model atmospheres with magnetic line blanketing

Model atmospheres of A and B stars are computed taking into account magnetic line blanketing. These calculations are based on the new stellar model atmosphere code LLModels which implements direct treatment of the opacities due to the bound-bound transitions and ensures an accurate and detailed description of the line absorption. The anomalous Zeeman effect was calculated for the field strengths between 1 and 40 kG and a field vector perpendicular to the line of sight. The model structure, high-resolution energy distribution, photometric colors, metallic line spectra and the hydrogen Balmer line profiles are computed for magnetic stars with different metallicities and are discussed with respect to those of non-magnetic reference models. The magnetically enhanced line blanketing changes the atmospheric structure and leads to a redistribution of energy in the stellar spectrum. The most noticeable feature in the optical region is the appearance of the 5200 A depression. However, this effect is prominent only in cool A stars and disappears for higher effective temperatures. The presence of a magnetic field produces opposite variation of the flux distribution in the optical and UV region. A deficiency of the UV flux is found for the whole range of considered effective temperatures, whereas the ``null wavelength'' where flux remains unchanged shifts towards the shorter wavelengths for higher temperatures.Comment: accepted by Astronomy & Astrophysic

Stellar model atmospheres with magnetic line blanketing. III. The role of magnetic field inclination

Context. See abstract in the paper. Aims. In the last paper of this series we study the effects of the magnetic field, varying its strength and orientation, on the model atmosphere structure, the energy distribution, photometric colors and the hydrogen Balmer line profiles. We compare with the previous results for an isotropic case in order to understand whether there is a clear relation between the value of the magnetic field angle and model changes, and to study how important the additional orientational information is. Also, we examine the probable explanation of the visual flux depressions of the magnetic chemically peculiar stars in the context of this work. Methods. We calculated one more grid of the model atmospheres of magnetic A and B stars for different effective temperatures (Teff=8000K, 11000K, 15000K), magnetic field strengths (B=0, 5, 10, 40 kG) and various angles of the magnetic field (Omega=0-90 degr) with respect to the atmosphere plane. We used the LLmodels code which implements a direct method for line opacity calculation, anomalous Zeeman splitting of spectral lines, and polarized radiation transfer. Results. We have not found significant changes in model atmosphere structure, photometric and spectroscopic observables or profiles of hydrogen Balmer lines as we vary the magnetic field inclination angle Omega. The strength of the magnetic field plays the main role in magnetic line blanketing. We show that the magnetic field has a clear relation to the visual flux depressions of the magnetic CP stars. Conclusions. See abstract in the paper.Comment: 10 pages, 5 figure

Turbulent convection: comparing the moment equations to numerical simulations

The non-local hydrodynamic moment equations for compressible convection are compared to numerical simulations. Convective and radiative flux typically deviate less than 20% from the 3D simulations, while mean thermodynamic quantities are accurate to at least 2% for the cases we have investigated. The moment equations are solved in minutes rather than days on standard workstations. We conclude that this convection model has the potential to considerably improve the modelling of convection zones in stellar envelopes and cores, in particular of A and F stars.Comment: 10 pages (6 pages of text including figure captions + 4 figures), Latex 2e with AAS Latex 5.0 macros, accepted for publication in ApJ

Critical evaluation of magnetic field detections reported for pulsating B-type stars in the light of ESPaDOnS, Narval and reanalyzed FORS1/2 observations

Recent spectropolarimetric studies of 7 SPB and $\beta$ Cep stars have suggested that photospheric magnetic fields are more common in B-type pulsators than in the general population of B stars, suggesting a significant connection between magnetic and pulsational phenomena. We present an analysis of new and previously published spectropolarimetric observations of these stars. New Stokes $V$ observations obtained with the high-resolution ESPaDOnS and Narval instruments confirm the presence of a magnetic field in one of the stars ($\epsilon$ Lup), but find no evidence of magnetism in 5 others. A re-analysis of the published longitudinal field measurements obtained with the low-resolution FORS1/2 spectropolarimeters finds that the measurements of all stars show more scatter from zero than can be attributed to Gaussian noise, suggesting the presence of a signal and/or systematic under-estimation of error bars. Re-reduction and re-measurement of the FORS1/2 spectra from the ESO archive demonstrates that small changes in reduction procedure lead to substantial changes in the inferred longitudinal field, and substantially reduces the number of field detections at the 3$\sigma$ level. Furthermore, we find that the published periods are not unique solutions to the time series of either the original or the revised FORS1/2 data. We conclude that the reported field detections, proposed periods and field geometry models for $\alpha$ Pyx, 15 CMa, 33 Eri and V1449 Aql are artefacts of the data analysis and reduction procedures, and that magnetic fields at the reported strength are no more common in SPB/$\beta$ Cep stars than in the general population of B stars.Comment: 10 pages, 5 figures, accepted for publication in ApJ, 2012, typo correcte

Electronic States in Diffused Quantum Wells

In the present study we calculate the energy values and the spatial distributions of the bound electronic states in some diffused quantum wells. The calculations are performed within the virtual crystal approximation, $sp^3 s^*$ spin dependent empirical tight-binding model and the surface Green function matching method. A good agreement is found between our results and experimental data obtained for AlGaAs/GaAs quantum wells with thermally induced changes in the profile at the interfaces. Our calculations show that for diffusion lengths $L_{D}=20\div100$ {\AA} the transition (C3-HH3) is not sensitive to the diffusion length, but the transitions (C1-HH1), (C1-LH1), (C2-HH2) and (C2-LH2) display large "blue shifts" as L_{D} increases. For diffusion lengths $L_{D}=0\div20$ {\AA} the transitions (C1-HH1) and (C1-LH1) are less sensitive to the L_{D} changes than the (C3-HH3) transition. The observed dependence is explained in terms of the bound states spatial distributions.Comment: ReVTeX file, 7pp., no macros, 4 figures available on the reques

Investigating the post-stimulus undershoot of the BOLD signal – A simultaneous fMRI and fNIRS study

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Near-infrared spectroscopy can detect brain activity during a color-word matching Stroop task in an event-related design

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Predictors of Stunting, Wasting and Underweight among Tanzanian Children Born to HIV-Infected Women.

Children born to human immunodeficiency virus (HIV)-infected women are susceptible to undernutrition, but modifiable risk factors and the time course of the development of undernutrition have not been well characterized. The objective of this study was to identify maternal, socioeconomic and child characteristics that are associated with stunting, wasting and underweight among Tanzanian children born to HIV-infected mothers, followed from 6 weeks of age for 24 months. Maternal and socioeconomic characteristics were recorded during pregnancy, data pertaining to the infant's birth were collected immediately after delivery, morbidity histories and anthropometric measurements were performed monthly. Multivariate Cox proportional hazards methods were used to assess the association between potential predictors and the time to first episode of stunting, wasting and underweight. A total of 2387 infants (54.0% male) were enrolled and followed for a median duration of 21.2 months. The respective prevalence of prematurity (<37 weeks) and low birth weight (<2500 g) was 15.2% and 7.0%; 11.3% of infants were HIV-positive at 6 weeks. Median time to first episode of stunting, wasting and underweight was 8.7, 7.2 and 7.0 months, respectively. Low maternal education, few household possessions, low infant birth weight, child HIV infection and male sex were all independent predictors of stunting, wasting and underweight. In addition, preterm infants were more likely to become wasted and underweight, whereas those with a low Apgar score at birth were more likely to become stunted. Interventions to improve maternal education and nutritional status, reduce mother-to-child transmission of HIV, and increase birth weight may lower the risk of undernutrition among children born to HIV-infected women